Public-key quantum money cannot be information-theoretically secure, it has to be based on a computational assumption. There have been many attempts at building a secure public-key quantum money scheme. Farhi et al. [1]} proposed a scheme based on knot theory. A banknote in their scheme consists of a quantum state \(\rho _s\)  representing a superposition of certain grid diagrams, and serial number \(s\)  which is the Alexander polynomial of the grids in \(\rho _s\) . A banknote is verified using a procedure based on a classical Markov chain.
